Sparse Gröbner bases

DOI10.1145/2608628.2608663zbMath1325.68278arXiv1402.7205OpenAlexW3098862099MaRDI QIDQ3452392

Pierre-Jean Spaenlehauer, Jean-Charles Faugère, Jules Svartz

Publication date: 11 November 2015

Published in: Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.7205

zbMATH Keywords

Gröbner basessparse polynomial systemstoric rings\(F_{5}\) algorithmFGLM

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Solving polynomial systems; resultants (13P15)

Related Items (7)

Random sampling in computational algebra: Helly numbers and violator spaces ⋮ Learning a performance metric of Buchberger's algorithm ⋮ On the complexity of solving generic overdetermined bilinear systems ⋮ Dimension results for extremal-generic polynomial systems over complete toric varieties ⋮ Chordal graphs in triangular decomposition in top-down style ⋮ Exploiting Chordal Structure in Polynomial Ideals: A Gröbner Bases Approach ⋮ Guessing Gröbner bases of structured ideals of relations of sequences

Uses Software

• slimgb
• Jordan

Cites Work

• An effective implementation of symbolic-numeric cylindrical algebraic decomposition for quantifier elimination
• Cylindrical algebraic decomposition using validated numerics
• The Jordan Curve Theorem, Formally and Informally
• On Computable Numbers, with an Application to the Entscheidungsproblem
• Definability and decision problems in arithmetic
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